GDP growth rates as confined L\'evy flights

TL;DR

This paper introduces a novel economic growth model using Le9vy-stable fluctuations within a confining potential, linking microscopic firm shocks to macroeconomic GDP dynamics and explaining observed business cycles.

Contribution

It presents a new framework combining microscopic firm-level shocks with macroscopic GDP fluctuations using Le9vy processes and confining potentials, bridging micro and macroeconomic analysis.

Findings

Model aligns well with 200 years of US GDP data.

Captures bimodal distribution of economic output, representing business cycles.

Demonstrates how firm-level shocks influence overall economic fluctuations.

Abstract

A new model that combines economic growth rate fluctuations at the microscopic and macroscopic level is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector level. We describe such fluctuations as independent L\'evy-stable fluctuations, varying over multiple orders of magnitude. These fluctuations are aggregated and measured at the macroscopic level in averaged economic output quantities such as GDP. A fundamental question is thereby to what extend individual firm size fluctuations can have a noticeable impact on the overall economy. We argue that this question can be answered by considering the L\'evy fluctuations as embedded in a steep confining potential well, ensuring nonlinear mean-reversal behavior, without having to rely on microscopic details of the system. The steepness of the potential well directly controls the extend towards which idiosyncratic shocks to firms and sectors are damped at the level of the economy. Additionally, the theory naturally accounts for business cycles, represented in terms of a bimodal economic output distribution, and thus connects two so far unrelated fields in economics. By analyzing 200 years of US GDP growth rates, we find that the model is in good agreement with the data.